While you are on this study, you will receive chemotherapy as part of your standard treatment. All participants will receive at least 2 cycles of adriamycin and ifosfamide chemotherapy (AI). A cycle is 3 weeks long. You may receive up to 6 cycles of adriamycin and ifosfamide. Adriamycin will be given as one large injection through a central venous catheter (plastic tube and needle placed under the collarbone) on Day 0. Ifosfamide will be given over 3 hours every day for 4 days (Days 0-3). Zinecard will be given as one large injection through the catheter on Day 0. Mesna will be given as a 24-hour infusion every day for 4 days through the same catheter (Days 0-3). Zinecard and mesna are given as standard of care. Zinecard is used to protect against heart-related side effects. Mesna is used to protect against bladder-related side effects. For patients with certain types of sarcoma, vincristine will be given through the catheter by rapid infusion on Day 0 only.